## Learning Mathematics for Teaching (LMT)

Research on teacher learning has suffered from a number of chronic methodological difficulties. Despite repeated calls for improved scholarship and more empirically grounded policy recommendations, the field been constrained by what scholars have been able to measure: characteristics of the learning opportunities themselves; teacher attitudes and beliefs which result from those opportunities; and, to some extent, teacher practices which emerge after such encounters. Typically left unmeasured, however, is a component which mediates each of these and is itself a significant target of many interventions, namely, teachers' content knowledge. The project proposed here would aim to help redress this problem in the area of K-8 mathematics, building on previous work to continue developing measures of teachers' mathematical knowledge for teaching. These measures will then be made available to MSP mathematics projects in hopes of improving the evaluation of those with programs for teacher learning and preparation.

Five categories of work are proposed:

- expanding existing measures upward to capture middle grade mathematics content for teaching, and developing new measures in key content areas;
- validating these measures through interviews with MSP participants and other teachers, reviews by mathematicians and mathematics educators, and other means;
- supporting high-quality uses of these measures via tools (database, core scales) and technical assistance to MSP evaluators;
- building a self-sustaining system of measures use; and
- building and testing theory through piloting and validation work. As these five aspects of work progress, we will carefully consider issues of equity, both from the theoretical and measurement perspectives. We will also consult with measurement and statistical experts to promote the production of the most technically sound and valid measures possible.

Intellectual Merit

This proposal will help advance knowledge and understanding in two related fields: in defining the component elements of knowledge for teaching K-8 mathematics, and in understanding the effects of professional development meant to improve that knowledge. The authors are qualified to do this work through their past experiences with theory and measures development, and have laid out a careful plan of instrument development over a five-year period.

Broader Impact

This proposal enhances the infrastructure for research into teacher professional development. Based on interest in existing measures, the authors expect these measures to be useful not only to MSPs, but also to others who seek to understand teacher learning. These measures can be used to evaluate teachers' learning in pre-service teacher education programs; to make comparisons between preparation in traditional teacher education programs and alternative routes to certification; to judge the efficacy of professional development aimed at improving teachers' content knowledge for teaching; and to estimate the effects of curriculum materials designed to improve teachers' knowledge of mathematics and students. Finally, this project contributes fundamentally to theory development, asking the question, "What do teachers need to know and be able to do with mathematics in order to teach mathematics?" By answering this question through item-writing and psychometric analyses as work progresses, the authors seek to contribute to progress in theory, practice, and policy in this field.